Motion in a Plane Questions and Answers Part-8

1. An aeroplane is flying with a uniform speed of 100 m/s along a circular path of radius 100 m. the angular speed of the aeroplane will be
a) 1 rad/sec
b) 2 rad/sec
c) 3 rad/sec
d) 4 rad/sec

Answer: a

2. A body moves with constant angular velocity on a circle. Magnitude of angular acceleration
a) \[r\omega^{2}\]
b) Constant
c) Zero
d) None of the above

Answer: c

3. What is the value of linear velocity, if \[\vec{\omega}=3\hat{i}-4\hat{j}+\hat{k}\]     and \[\vec{r}=5\hat{i}-6\hat{j}+6\hat{k}\]
a) \[6\hat{i}+2\hat{j}-3\hat{k}\]
b) \[-18\hat{i}-13\hat{j}+2\hat{k}\]
c) \[4\hat{i}-13\hat{j}+6\hat{k}\]
d) \[6\hat{i}-2\hat{j}+8\hat{k}\]

Answer: b

4. A stone is tied to one end of a string 50 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 10 revolutions in 20 s, what is the magnitude of acceleration of the stone
a) \[493cm\diagup s^{2}\]
b) \[720cm\diagup s^{2}\]
c) \[860cm\diagup s^{2}\]
d) \[990cm\diagup s^{2}\]

Answer: a

5. A 100 kg car is moving with a maximum velocity of 9 m/s across a circular track of radius 30 m. The maximum force of friction between the road and the car is
a) 1000 N
b) 706 N
c) 270 N
d) 200 N

Answer: c

6. The maximum speed of a car on a road–turn of radius 30 m, if the coefficient of friction between the tyres and the road is 0.4, will be
a) 10.84 m/sec
b) 9.84 m/sec
c) 8.84 m/sec
d) 6.84 m/sec

Answer: a

7. The angular velocity of a wheel is 70 rad/sec. If the radius of the wheel is 0.5 m, then linear velocity of the wheel is
a) 70 m/s
b) 35 m/s
c) 30 m/s
d) 20 m/s

Answer: b

8. A cyclist goes round a circular path of circumference 34.3 m in \[\sqrt{22}\] sec. the angle made by him, with the vertical, will be
a) \[45^{\circ}\]
b) \[40^{\circ}\]
c) \[42^{\circ}\]
d) \[48^{\circ}\]

Answer: a

9. A particle of mass M is moving in a horizontal circle of radius R with uniform speed V. When it moves from one point to a diametrically opposite point, its
a) Kinetic energy changes by \[MV^{2}\diagup 4\]
b) Momentum does not change
c) Momentum changes by 2MV
d) Kinetic energy changes by \[MV^{2}\]

Answer: c
Explanation: Momentum changes by 2MV

10. A ball of mass 0.1 Kg. is whirled in a horizontal circle of radius 1 m. by means of a string at an initial speed of 10 r.p.m. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is
a) 5 r.p.m.
b) 10 r.p.m.
c) 20 r.p.m.
d) 14 r.p.m.

Answer: a